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ABSTRACT
Development of a multimodal probability density function
The trend of DBH distribution is an excellent referential to the forest study, native or
manmade forests. Density Probability Functions can be satisfactorily used for that purpose.
Therefore, the main objective of this research was to present a new mathematical model,
sufficiently flexible to represent two or more modes. As objective of evaluating the model
effectiveness, its adjustment was compared to the classic continuous probabilistic
distributions (Gauss, Exponential, Gamma, Beta and Weibull), as well as Quadros and Spline
Function. Three distinct diametric distributions were used: one for Brazilian Nut tree, with
three modes and passing trough the origin, and two for Araucaria, with two modes, one
passing trough the origin and the other no. The Exponential Distribution assumes just a
decrescent form and is potentially viable when represent natural regeneration diametric data is
desirable; therefore it is not good to this research. The Gaussian Distribution, commonly used
to represent diametric distributions, provided a non satisfactory result, because of its low
flexibility, in which occur one mode. The Weibull, Gamma and Beta Distributions were more
flexible, but can not represent two or more modes. The model developed by Quadros is more
flexible, but it was not adherent to all data distributions observed in this work. The Spline
Function presented a high flexibility, but the results were not satisfactory, as considering the
adjustment, as considering the biological interpretation, since it generates negative
probabilities and can not predict the occurrence of individuals in the higher diameter classes.
The proposed model was adherent to all diametric distributions, being capable to present two
or more modes (easily implemented); it is flexible; it can or can not pass trough the origin; it
has all characteristics of a density probabilistic function (it is always positive, continuous and
can be integrated in its domain), the average and variance can be obtained by means of
calculus, according to the probabilistic distribution theory.
Keywords: Probability distribution, Mode, Forest, Araucaria angustifolia, Bertholletia
excelsa.